Early starter Flury found the perfect line down the sunlit Roc de Fer piste to win in one minute 28.03 seconds.
Austrian Nina Ortlieb (26) missed out on gold by an agonising 0.04 seconds with Swiss defending champion Corinne Suter 0.12 seconds back in the bronze medal position.
Italian Goggia was putting down a fast time as she looked to complete her personal set of championship medals after taking silver in super-G in 2019 and bronze in giant slalom in 2017.
But the 2018 Olympic champion made a big mistake in the lower section of the course and although she just avoided crashing, she hit a gate heavily and was disqualified.
"I'm more than disappointed I'm sorrowful because I won't be able to achieve a medal in this world championships and this hurts inside," Goggia, who wore a black armband after the death of former Italian racer Elena Fanchini, told Eurosport.
"But sport is this way. People expect you to win easily but that doesn't count. Life goes on and we move to the next races."
Flury's gold was an upset as she had not even managed a World Cup podium this season. It was also Switzerland's first gold of the championships so far.
"I still can't believe it, it's amazing and also with Corinne on the podium it's unbelievable," Flury said.
American Mikaela Shiffrin (27), who took her 12th career world championship medal with silver in the super-G, did not start.
Action continues on Sunday with the men's downhill.
